The present invention relates to blades for a steam turbine rotor. More specifically, the present invention relates to a blade for use in the last stage in a low pressure steam turbine.
The steam flow path of a steam turbine is formed by a stationary cylinder and a rotor. A large number of stationary vanes are attached to the cylinder in a circumferential array and extend inward into the steam flow path. Similarly, a large number of rotating blades are attached to the rotor in a circumferential array and extend outward into the steam flow path. The stationary vanes and rotating blades are arranged in alternating rows so that a row of vanes and the immediately downstream row of blades forms a stage. The vanes serve to direct the flow of steam so that it enters the downstream row of blades at the correct angle. The blade airfoils extract energy from the steam, thereby developing the power necessary to drive the rotor and the load attached to it.
The amount of energy extracted by each row of rotating blades depends on the size and shape of the blade airfoils, as well as the quantity of blades in the row. Thus, the shapes of the blade airfoils are an extremely important factor in the thermodynamic performance of the turbine and determining the geometry of the blade airfoils is a vital portion of the turbine design.
As the steam flows through the turbine its pressure drops through each succeeding stage until the desired discharge pressure is achieved. Thus, the steam properties--that is, temperature, pressure, velocity and moisture content--vary from row to row as the steam expands through the flow path. Consequently, each blade row employs blades having an airfoil shape that is optimized for the steam conditions associated with that row. However, within a given row the blade airfoil shapes are identical, except in certain turbines in which the airfoil shapes are varied among the blades within the row in order to vary the resonant frequencies.
The blade airfoils extend from a blade root used to secure the blade to the rotor. Conventionally, this is accomplished by imparting a fir tree shape to the root by forming approximately axially extending alternating tangs and grooves along the sides of the blade root. Slots having mating tangs and grooves are formed in the rotor disc. When the blade root is slid into the disc slot, the centrifugal load on the blade, which is very high due to the high rotational speed of the rotor--typically 3600 RPM for a steam turbine employed in electrical power generation, is distributed along portions of the tangs, referred to as bearing areas, over which the root and disc are in contact. Because of the high centrifugal loading, the stresses in the blade root and disc slot are very high. It is important, therefore, to minimize the stress concentrations formed by the tangs and grooves and maximize the bearing areas over which the contact forces between the blade root and disc slot occur. This is especially important in the latter rows of a low pressure steam turbine due to the large size and weight of the blades in these rows and the presence of stress corrosion due to moisture in the steam flow.
In addition to the steady centrifugal loading, the blades are also subject to vibration at frequencies which coincide with integer multiples, referred to as harmonics, of the rotor rotational frequency. Such blade vibration can be excited by non-uniformities in the steam flow around the circumference of the turbine. Non-uniformities in the steam flow can result from the presence of extraction pipes and reinforcing ribs or imperfections in the shape and spacing of the stationary vanes. Thus, in steam turbines that are intended to operate at or very near a single rotational frequency, the blades are designed such that one or more of their resonant frequencies do not coincide with harmonics of rotor rotational frequency, referred to as "tuning."
The difficulty associated with designing a steam turbine blade is exacerbated by the fact that the airfoil shape determines, in large part, both the forces imposed on the blade and its mechanical strength and resonant frequencies, as well as the thermodynamic performance of the blade. These considerations impose constraints on the choice of blade airfoil shape so that, of necessity, the optimum blade airfoil shape for a given row is a matter of compromise between its mechanical and aerodynamic properties.
It is therefore desirable to provide a row of steam turbine blades that provides good thermodynamic performance while minimizing the stresses on the blade airfoil and root due to centrifugal force and avoiding resonant excitation.